Education Commons^™

Threshold Concepts In Quantitative Reasoning, Judith Canner, Jennifer E. Clinkenbeard

Numeracy

The idea of “threshold concepts” has been used to identify discipline-based concepts that are critical to that academic area. Threshold concepts are often difficult for students to assimilate in a meaningful way but, once done, can be powerful for the learner. In general, threshold concepts are 1) transformative to learner thinking; 2) bounded by the discipline; 3) integrative with other concepts; and 4) irreversible once understood (Meyer and Land 2003). This paper presents five threshold concepts in quantitative reasoning (QR) developed by transdisciplinary faculty workgroups that may be applicable for non-mathematics disciplines as well. They are as follows: 1) QR …

Using Covid-19 Vaccine Efficacy Data To Teach One-Sample Hypothesis Testing, Frank Wang

Numeracy

In late November 2020, there was a flurry of media coverage of two companies’ claims of 95% efficacy rates of newly developed COVID-19 vaccines, but information about the confidence interval was not reported. This paper presents a way of teaching the concept of hypothesis testing and the construction of confidence intervals using numbers announced by the drug makers Pfizer and Moderna publicized by the media. Instead of a two-sample test or more complicated statistical models, we use the elementary one-proportion z-test to analyze the data. The method is designed to be accessible for students who have only taken a …

Three Formative Questions In The Quantitative Literacy Movement, Dorothy Wallace

Numeracy

In this essay we remember early discussions attempting to answer three questions that played a formative role in our understanding of and approach to numeracy, quantitative literacy, and quantitative reasoning: (1) What is numeracy? (2) Should the QL movement promote any specific kind of pedagogy? (3) What organizational structure will best support QL?

As the QL movement has progressed, these three questions continue to be difficult to answer. As a result, they have been useful formative guides for institutions and organizations seeking to improve the quantitative reasoning of students. Now that the quantitative literacy movement has a firmer standing in …

Developing Mathematics Teachers’ Attention To Quantitative Reasoning In Task Design: A Modeling Approach, David Glassmeyer

Numeracy

This study examines how a models-and-modeling perspective affected teachers' attention to quantitative reasoning in task design. A Model-Eliciting Activity (MEA) was implemented with 21 teachers over four weeks, challenging teachers to design a quantitative reasoning task for their students. Teachers’ initial quantitative reasoning tasks did not incorporate quantities or quantitative relationships, two essential components of quantitative reasoning. As teachers revised their tasks through the MEA, most teachers began attending to these components. This article details how a modeling approach to teacher education provided a method to describe and support teachers to incorporate quantitative reasoning in their classroom tasks, though attending …

Why I Believe People Need Painting By Numbers, Jason Makansi

Numeracy

Jason Makansi.2016. Painting By Numbers: How to Sharpen Your BS Detector and Smoke Out the Experts (Tucson AZ: Layla Dog Press). 196 pp. ISBN 978-0998425900.

This piece briefly introduces my Painting By Numbers, which aims to take the core messages of the QL/QR community from academic and professional circles to the rest of the citizenry. I describe the book in the context of the critical need for the most basic numeracy tools to help consumers of news, information, and analysis—delivered through traditional and contemporary social media outlets—determine where a reported numerical result lies on the scale from utter nonsense …

Quantitative Reasoning For Teachers: Explorations In Foundational Ideas And Pedagogy, Sheryl Stump

Numeracy

This note describes a course designed to prepare community college instructors and K-12 teachers for teaching foundational aspects of quantitative reasoning. A body of literature on quantitative reasoning and quantitative literacy informed the course design. The note describes the course content, which includes engaging in case studies, reading and discussion, writing assignments, group problem solving, and news-of-the-day presentations. Details of these assignments are provided. The capstone assignment for the course is for participants to design a set of case studies for their own students. Details of this assignment are also provided as well as specific examples of participants’ learning.